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Tytuł artykułu

Application of Transition Finite Elements in hpq-Adaptive Modeling and Analysis of Machine Elements

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper concerns the modeling and analysis of machine elements using the adaptive finite element method. The adaptation used is of hpq type, which means that the finite element dimension h and element transverse q and longitudinal p approximation order may be different in each element. These parameters are determined automatically by the program to obtain modeling and approximation error levels not higher than the assumed admissible level of the errors. The presented paper focuses on the use of transition elements between basic elements corresponding to the three-dimensional theory of elasticity and the first-order shell model. Three applied transition elements differ in their assumptions regarding the continuity of the displacement, strain, and stress fields between the basic models. The effectiveness of the application of transition elements was assessed in terms of the removal of the internal boundary layer at the boundary between the models and the convergence of adaptive solutions taking into account these models.
Rocznik
Tom
Strony
33--53
Opis fizyczny
Bibliogr. 28 poz., rys., wykr.
Twórcy
  • Department of Mechanics and Basics of Machine Design Faculty of Technical Sciences University of Warmia and Mazury in Olsztyn
  • Department of Mechanics and Basics of Machine Design Faculty of Technical Sciences University of Warmia and Mazury in Olsztyn
  • Institute of Fluid Flow Machinery Polish Academy of Sciences in Gdańsk
Bibliografia
  • AINSWORTH M., ODEN J.T. 1992. A procedure for a posteriori error estimation for h-p finite element methods. Computer Methods in Applied Mechanics and Engineering, 101: 73-96.
  • COFER W.F., WILL K.M. 1991. A Three-dimensional, Shell-solid transition element for general nonlinear analysis. Computers & Structures, 38: 449-462.
  • DÁVILA C.G.1994. Solid-to-shell transition elements for the computation of interlaminar stresses. Computing Systems in Engineering, 5: 193-202.
  • DEMKOWICZ L. 2006. Computing with hp-Adaptive Finite Elements. Volume I. One and Two-Dimensional Elliptic and Maxwell Problems. Chapman &Hall/CRC Press, Taylor and Francis Group, Boca Raton.
  • GMÜR T.C., SCHORDERET A.M. 1993. A set of three-dimensional solid to shell transition elements for structural dynamics. Computers & Structures, 46: 583-591.
  • HUANG F., XIE X. 2011. A Modified Nonconforming 5-Node Quadrilateral Transition Finite Element. Advances in Applied Mathematics and Mechanics, 2: 784-797.
  • JEYACHANDRABOSE C., KIRKHOPE J. 1984. Construction of transition finite elements for the plane triangular family. Computers & Structures, 18: 1127-1134.
  • NOSARZEWSKA M. 2007. Zastosowanie elementów przejściowych w adaptacyjnej analizie struktur sprężystych. Praca magisterska. Wydział Nauk Technicznych, Uniwersytet Warmińsko-Mazurski, Olsztyn.
  • NOSARZEWSKA M., ZBOIŃSKI G. 2009. Efektywność przejściowych elementów skończonych w hierarchicznym modelowaniu struktur złożonych. Modelowane Inżynierskie, 7(38): 131-138.
  • ODEN J.T. 1993. Error estimation and control in computational fluid dynamics. The O.C. Zienkiewicz Lecture. Proc. Math. of Finite Elements - MAFELAP VIII, 1-36. Brunnel Univ., Uxbridge.
  • ODEN J.T, CHO J.R. 1996. Adaptive hpq-finite element methods of hierarchical models for plate- and shell-like structures. Computer Methods in Applied Mechanics and Engineering, 136: 317-345.
  • RANK E., BABUŠKA I. 1987. An expert system for the optimal mesh design in the hp-version of the finite element method. International Journal for Numerical Methods in Engineering, 24: 2087-2106.
  • SCHWAB C. 1998. p and hp FEM. Oxford University Press, Oxford.
  • SURANA K.S. 1980. Transition finite elements for three-dimensional stress analysis. International Journal for Numerical Methods in Engineering, 15: 991-1020.
  • SURANA K.S. 1982. Geometrically non-linear formulation for the three dimensional solid-shell transition finite elements. Computers & Structures, 15: 549-566.
  • SURANA K.S. 1983. Geometrically nonlinear formulation for the axi-simetric transition finite element. Computers & Structures, 17: 243-255.
  • SURANA K.S. 1987. Three dimensional solid-shell transition finite elements for heat conduction. Computers & Structures, 26: 941-950.
  • SZABÓ B.A., SAHRMANN G.J. 1998, Hierarchic plate and shell models based on p-extension. International Journal for Numerical Methods in Engineering, 26: 1855-1881.
  • WAN K.H. 2004. Transition finite elements for mesh refinement in plane and plate Bendig analyses. MSc Thesis. Mechanical Engineering Department, The University of Hong Kong.
  • ZBOIŃSKI G. 1997. Application of the three-dimensional triangular-prism hpq adaptive finite element to plate shell analysis. Computers and Structures, 65(4): 497-514.
  • ZBOIŃSKI G. 2001. Modelowanie hierarchiczne i metoda elementów skończonych do adaptacyjnej analizy struktur złożonych. Zeszyty Naukowe IMP PAN w Gdańsku. Studia i Materiały. Instytut Maszyn Przepływowych PAN, Gdańsk.
  • ZBOIŃSKI G. 2010. Adaptive hpq finite element methods for the analysis of 3D-based models of complex structures. Part 1. Hierarchical modeling and approximation. Computer Methods in Applied Mechanics and Engineering, 199: 2913-2940.
  • ZBOIŃSKI G. 2013. Adaptive hpq finite element methods for the analysis of 3D-based models of complex structures. Part 2. A posteriori error estimation. Computer Methods in Applied Mechanics and Engineering, 267: 531-565.
  • ZBOIŃSKI G., JASIŃSKI M. 2007. 3D-based hp-adaptive first-order shell finite element for modelling and analysis of complex structures. Part 1. The model and the approximation. International Journal for Numerical Methods in Engineering, 70: 1513-1545.
  • ZBOIŃSKI G., OSTACHOWICZ W. 2000. An algorithm of a family of 3D-based, solid-to-shell, hpq/hp-adaptive finite elements. Journal of Theoretical and Applied Mechanics, 38: 791-806.
  • ZIELIŃSKA M., ZBOIŃSKI G. 2013. Opracowanie efektywnego numerycznie sformułowania adaptacyjnego, opartego na podejściu trójwymiarowym, bryłowo-powłokowego elementu przejściowego zapewniającego ciągłość pola naprężeń pomiędzy modelami podstawowymi. Raport wewnętrzny, nr arch. 324/15, Instytut Maszyn Przepływowych PAN, Gdańsk.
  • ZIELIŃSKA M., ZBOIŃSKI G. 2014a. Analiza płyt i powłok zdominowanych membranowo z ciągłą zmianą naprężeń i odkształceń w strefach przejściowych. Mechanik, 87: 855-872.
  • ZIELIŃSKA M., ZBOIŃSKI G. 2014b. hp-Adaptive finite element analysis of thin-walled structures with use of the shell-to-shell transition elements. In: Recent Advances in Computational Mechanics. Eds. T. Lodygowski, J. Rakowski, P, Litewka. CRC Press, London.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8b475bf1-0e38-4935-b886-19aadc902953
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